1.2 Scoring System, Penalty Mathematics & Strategic Answering

1.2 Scoring System, Penalty Mathematics & Strategic Answering

Key Exam Fact: Bocconi applies negative marking: +1.00 point for a correct answer, 0.00 for an omitted answer, and −0.20 for a wrong answer — or −0.33 on critical-thinking items that offer only three options. Applicants whose total score, penalties included, is lower than 17 are not considered in the selection process. Applicants who list the Bachelor in Mathematical and Computing Sciences for Artificial Intelligence must additionally obtain at least 11 points out of 24 in the Mathematics area.

Standardised tests generally choose one of two philosophies: rights-only scoring, where a wrong answer costs nothing and blanket guessing is rational, or negative marking, where it is not. Bocconi uses negative marking. The purpose is to penalise reckless guessing and to test judgement under uncertainty. Because the Online Bocconi Test is also forward-only — three questions per screen, no return to earlier screens — every guess-or-skip decision is made once and cannot be revised. Getting the arithmetic of that decision right is worth several points.

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The Official Scoring Formula

Your final score out of 50 is:

$\text{Score} = (1.00 \times C) - (0.20 \times W_{5}) - (0.33 \times W_{3}) + (0.00 \times B)$

Where:

• $C$ is the number of correct answers, each worth $+1.00$.
• $W_{5}$ is the number of wrong answers on standard items, which present five options and carry a $-0.20$ penalty.
• $W_{3}$ is the number of wrong answers on the three-option critical-thinking items, which carry a $-0.33$ penalty.
• $B$ is the number of omitted questions, each worth exactly $0.00$.

Scoring Scenario Comparison

Four candidates who divide their 50 questions differently between answered and omitted:

Compare C and D. Both knew exactly 21 answers. C guessed on 24 further questions, surrendered 4.80 points, and fell below the exclusion floor. D left the hopeless items blank, kept 19.00, and stayed in the selection. Same knowledge, opposite outcome.

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Expected Value: When Is a Guess Worth Making?

Expected value is the average points a decision returns if you made it many times:

$\mathbb{E}[X] = \sum_{i=1}^{n} P(x_i) \cdot x_i$

Here the payoffs are $+1.00$ for a correct answer and $-0.20$ (or $-0.33$) for a wrong one.

1. Blind Guessing

• Standard five-option item ($p = 0.20$, penalty $-0.20$): $\mathbb{E}[\text{Blind}_5] = (0.20 \times 1.00) + (0.80 \times -0.20) = 0.20 - 0.16 = +0.04$
• Three-option critical-thinking item ($p = 1/3$, penalty $-0.33$): $\mathbb{E}[\text{Blind}_3] = (0.333 \times 1.00) + (0.667 \times -0.33) = 0.333 - 0.220 = +0.113$

The Blind-Guessing Paradox

Both numbers are positive, because Bocconi's penalties are gentler than the mathematically neutral correction (which would be $-0.25$ on a five-option item and $-0.50$ on a three-option item). So why is blanket guessing still a bad plan?

1. Variance is brutal over small samples. Across ten blind guesses on five-option items you expect two right and eight wrong, worth $2.00 - 1.60 = +0.40$ points. One unlucky run of zero right and ten wrong costs you $-2.00$ — five times the upside you were playing for.
2. The 17-point floor is a cliff, not a slope. Near the exclusion threshold, downside variance does not cost you rank; it costs you the entire application.
3. Time is the real currency. With no way back to an earlier screen, seconds burned reading a question you cannot touch are seconds stolen from a question on the same screen that you could have solved outright.

2. Educated Guessing: The Mathematics of Elimination

Guessing after eliminating at least one provably wrong option is not merely acceptable; on this test it is mandatory. Watch the expected value climb:

The two decisive rows are the ones where a coin-flip remains. Reduce a five-option item to two candidates and the expected value is $+0.40$; reduce a three-option critical-thinking item to two and it is $+0.335$. Do that on ten questions across the test and the statistically expected return is:

$\text{Net gain} = (5 \times 1.00) - (5 \times 0.20) = 5.00 - 1.00 = +4.00 \text{ points}$

Four points is eight per cent of the whole scale. On a merit ranking, that is not a rounding error.

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The 17-Point Exclusion Floor

The official rule: applicants who receive a total score, penalties included, lower than 17 will not be considered in the selection process. Bocconi repeats the threshold in its results guidance: a score of 17 or higher is the minimum required to apply.

Three Things Candidates Get Wrong About the Floor

1. It applies to the penalised score, not to the raw count of correct answers. Twenty correct answers with sixteen wrong is $20 - (16 \times 0.20) = 16.80$ — below the floor, despite twenty correct answers.
2. Nothing compensates for it. An outstanding secondary-school record does not rescue a score of 16.80, because the application never reaches the ranking stage.
3. It changes your tactics in real time. A candidate who reaches the halfway screens confident of only about twenty answers should switch from maximising expected value to protecting the floor: take the guesses where two options remain, and take none of the others.

The Mathematics Sub-Score Requirement

Bocconi publishes exactly one programme-specific sub-score rule for the standard test: applicants who have the Bachelor in Mathematical and Computing Sciences for Artificial Intelligence among their choices must obtain at least 11 points out of 24 in the Mathematics area to be considered for that programme. This is a second, independent hurdle — clearing 17 overall does not clear it. The Test Score Report, available in your platform area within 48 hours of the test, reports the score achieved in each subject area, so you can verify your Mathematics sub-score directly rather than estimating it.

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How the Test Score Is Actually Used

Bocconi's selection is arithmetic, not holistic. It is based on exactly two elements:

1. Selection test score — 55%. This may be the Online Bocconi Test, or the SAT or ACT. (The Online Bocconi Test – Law and the LSAT are accepted only for Law School programmes.)
2. Third-last and second-last secondary-school year GPA — 45%.

Two details matter for planning:

• Bocconi states that no other document is considered — recommendation letters, motivational letters, CVs and résumés play no part in the assessment.
• The GPA years are the third-last and second-last years, counted backwards from the year of the diploma. Bocconi states explicitly that mid-year grades, grades from the final year of secondary school and predicted grades are NOT considered. Only the final grades of those two earlier years count.

Because the SAT and ACT are accepted alternatives and the application portal takes the highest score among the reports you upload, a candidate who has already sat the SAT is not obliged to make the Bocconi test their best result — but they do need one qualifying result.

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What Bocconi Publishes About "A Good Score" — and What It Does Not

Be careful here, because this is where most third-party guidance invents numbers.

Published by Bocconi:

• A score below 17 excludes the applicant.
• A score of 17 or higher makes the result usable in an application.
• The AI bachelor additionally requires 11/24 in Mathematics.
• The test counts for 55% of the evaluation, GPA for 45%.

Not published by Bocconi: any programme-by-programme cut-off, any admitted-candidate score distribution, and any "competitive score" figure. Admission thresholds emerge from the ranking of each selection round and are not announced in advance, so any table that maps specific scores onto specific programmes is an estimate, not a rule.

That still leaves you needing a preparation target. Use the following as OpenExamPrep practice benchmarks — deliberately conservative goals for your own mock scoring, not Bocconi figures:

Because the ranking is competitive and unpublished, the honest strategic advice is simple: your score is your only lever, so maximise it rather than aiming at a number someone on a forum told you was enough.

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The Decision Engine: Answer or Omit, Once and for All

On a forward-only test, "I'll come back to it" is not a decision. Run this sequence on each of the three questions on a screen.

1. Twenty-second triage. Do you recognise the theorem, identity or item type?
   • Yes: solve it, holding to the screen's 4 minute 30 second total budget.
   • No: go to step 2 immediately.
2. Elimination filter. Can you rule out at least one option through a sign check, a boundary or order-of-magnitude check, a dimensional check, or a direct contradiction with the passage or data?
   • Two or three options left: answer. The expected value is $+0.20$ to $+0.40$.
   • Four or five options left, none eliminable: go to step 3.
3. Floor check. Are you comfortably clear of 17 for this test?
   • Yes, and you have spare seconds on this screen: a blind answer is very slightly positive; take it rather than leaving the seconds unused, since there is no later phase to spend them in.
   • No, or the screen clock is tight: leave it blank and give the seconds to the other two questions on the same screen. Protecting the floor and protecting the screen budget point the same way.
4. Five-second confirmation sweep. Before clicking Next, check that each of the three items displays the option you meant to select — including the ones you decided to leave blank on purpose.

The asymmetry to internalise: an answer you never recorded is worth 0.00, while a solved question on the same screen is worth 1.00. Time redistributed from a hopeless question to a solvable one on the same screen is the highest-return trade available on this test.